Adaptive dimensional reduction and divergence stability

There has been increased interest recently in feed-back methods for reliable, robust, efficient computational methods in mechanics. We will outline the construction of such methods for a class of problems describing bending of plates for certain classes of loads. We emphasize the theoretical performance of this method, such as the selection of basis functions in the dimensional reduction – ensuring optimal convergence rates in the “thin” limit as well as in the order of model increasing. We then discuss the feasibility of efficient solution of the first couple of members of the sequence of models – also with an eye towards reliability and adaptivity.